Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Part D Please

2. Prove the following, using induction: (a) If an+1 = an/(an +1) prove that an = ao/(nao+1) for all n ≥ 0. (b) Define fo = 0, f₁ = 1 and fn = fn-1 + fn-2 for n ≥ 2. Show that 3 fak for all k ≥ 0. (c) Show that for 2" > 4n for n > 5. (d) Show that 3 | 5 - 2" for all n. (e) Show that every n ≥ 8 can be written as 3a+5b for some a, b € N.
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Transcribed Image Text:2. Prove the following, using induction: (a) If an+1 = an/(an +1) prove that an = ao/(nao+1) for all n ≥ 0. (b) Define fo = 0, f₁ = 1 and fn = fn-1 + fn-2 for n ≥ 2. Show that 3 fak for all k ≥ 0. (c) Show that for 2" > 4n for n > 5. (d) Show that 3 | 5 - 2" for all n. (e) Show that every n ≥ 8 can be written as 3a+5b for some a, b € N.
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